The present invention relates to a method and apparatus which uses model-based adaptive filtering techniques to estimate physiological parameters. More specifically, the invention employs Kalman filtering techniques in pulse oximetry to estimate the oxygen saturation of hemoglobin in arterial blood.
Pulse oximeters typically measure and display various blood flow characteristics including but not limited to the oxygen saturation of hemoglobin in arterial blood. Oximeters pass light through blood perfused tissue such as a finger or an ear, and photoelectrically sense the absorption of light in the tissue. The amount of light absorbed is then used to calculate the amount of the blood constituent (e.g., oxyhemoglobin) being measured.
The light passed through the tissue is selected to be of one or more wavelengths that are absorbed by the blood in an amount representative of the amount of the blood constituent present in the blood. The amount of light passed through the tissue varies in accordance with the changing amount of blood constituent in the tissue and the related light absorption.
When the measured blood parameter is the oxygen saturation of hemoglobin, a convenient starting point assumes a saturation calculation based on Lambert-Beer's law. The following notation will be used herein:I(λ, t)=Io(λ)exp(−(sβo(λ)+(1−s)βr(λ))l(t))   (1)where:                λ=wavelength;        t=time;        I=intensity of light detected;        Io=intensity of light transmitted;        s=oxygen saturation;        βo, βr=empirically derived absorption coefficients; and        l(t)=a combination of concentration and path length from emitter to detector as a function of time.The traditional approach measures light absorption at two wavelengths, e.g., red and infrared (IR), and then calculates saturation by solving for the “ratio of ratios” as follows.        1. First, the natural logarithm of (1) is taken (“log” will be used to represent the natural logarithm) for IR and RedlogI=logIo−(sβo+(1−s)βr)l   (2)        2. (2) is then differentiated with respect to time        
                                                        ⅆ              log                        ⁢                                                  ⁢            I                                ⅆ            t                          =                              -                          (                                                s                  ⁢                                                                          ⁢                                      β                    o                                                  +                                                      (                                          1                      -                      s                                        )                                    ⁢                                      β                    r                                                              )                                ⁢                                    ⅆ              l                                      ⅆ              t                                                          (        3        )                            3. Red (3) is divided by IR (3)        
                                                        ⅆ              log                        ⁢                                                  ⁢                                          I                ⁡                                  (                                      λ                    R                                    )                                            /                              ⅆ                t                                                                        ⅆ              log                        ⁢                                                  ⁢                                          I                ⁡                                  (                                      λ                    IR                                    )                                            /                              ⅆ                t                                                    =                                            s              ⁢                                                          ⁢                                                β                  o                                ⁡                                  (                                      λ                    R                                    )                                                      +                                          (                                  1                  -                  s                                )                            ⁢                                                β                  r                                ⁡                                  (                                      λ                    R                                    )                                                                                        s              ⁢                                                          ⁢                                                β                  o                                ⁡                                  (                                      λ                    IR                                    )                                                      +                                          (                                  1                  -                  s                                )                            ⁢                                                β                  r                                ⁡                                  (                                      λ                    IR                                    )                                                                                        (        4        )                            4. Solving for s        
  s  =                                                        ⅆ              log                        ⁢                                                  ⁢                          I              (                              λ                IR                            )                                            ⅆ            t                          ⁢                              β            r                    ⁡                      (                          λ              R                        )                              -                                                  ⅆ              log                        ⁢                                                  ⁢                          I              (                              λ                R                            )                                            ⅆ            t                          ⁢                              β            r                    ⁡                      (                          λ              IR                        )                                                                                  ⅆ              log                        ⁢                                                  ⁢                          I              (                              λ                R                            )                                            ⅆ            t                          ⁢                  (                                                    β                o                            ⁡                              (                                  λ                  IR                                )                                      -                                          β                r                            ⁡                              (                                  λ                  IR                                )                                              )                    -                                                  ⅆ              log                        ⁢                                                  ⁢                          I              (                              λ                IR                            )                                            ⅆ            t                          ⁢                  (                                                    β                o                            ⁡                              (                                  λ                  R                                )                                      -                                          β                r                            ⁡                              (                                  λ                  R                                )                                              )                    Note in discrete time
                    ⅆ        log            ⁢                          ⁢              I        ⁡                  (                      λ            ,            t                    )                            ⅆ      t        ≅            log      ⁢                          ⁢              I        ⁡                  (                      λ            ,                          t              2                                )                      -          log      ⁢                          ⁢              I        ⁡                  (                      λ            ,                          t              1                                )                    Using log A−log B=log A/B,
                    ⅆ        log            ⁢                          ⁢              I        ⁡                  (                      λ            ,            t                    )                            ⅆ      t        ≅      log    ⁡          (                        I          ⁡                      (                                          t                2                            ,              λ                        )                                    I          ⁡                      (                                          t                1                            ,              λ                        )                              )      So, (4) can be rewritten as
                                                                        ⅆ                log                            ⁢                                                          ⁢                              I                ⁡                                  (                                      λ                    R                                    )                                                                    ⅆ              t                                                                          ⅆ                log                            ⁢                                                          ⁢                              I                ⁡                                  (                                      λ                    IR                                    )                                                                    ⅆ              t                                      ≅                              log            ⁡                          (                                                I                  ⁡                                      (                                                                  t                        1                                            ,                                              λ                        R                                                              )                                                                    I                  ⁡                                      (                                                                  t                        2                                            ,                                              λ                        R                                                              )                                                              )                                            log            ⁡                          (                                                I                  ⁡                                      (                                                                  t                        1                                            ,                                              λ                        IR                                                              )                                                                    I                  ⁡                                      (                                                                  t                        2                                            ,                                              λ                        IR                                                              )                                                              )                                      ≡        R                            (        5        )            where R represents the “ratio of ratios.”Solving (4) for s using (5) gives
  s  =                                          β            r                    ⁡                      (                          λ              R                        )                          -                  R          ⁢                                          ⁢                                    β              r                        ⁡                          (                              λ                IR                            )                                                            R          ⁡                      (                                                            β                  o                                ⁡                                  (                                      λ                    IR                                    )                                            -                                                β                  r                                ⁡                                  (                                      λ                    IR                                    )                                                      )                          -                              β            o                    ⁡                      (                          λ              R                        )                          +                              β            r                    ⁡                      (                          λ              R                        )                                .  
From (5) note that R can be calculated using two points (e.g., plethysmograph maximum and minimum), or a family of points. One method using a family of points uses a modified version of (5). Using the relationship
                                                        ⅆ              log                        ⁢                                                  ⁢            I                                ⅆ            t                          =                                            ⅆ              I                        /                          ⅆ              t                                I                                    (        6        )            now (5) becomes
                                                                                                                                    ⅆ                      log                                        ⁢                                                                                  ⁢                                          I                      ⁡                                              (                                                  λ                          R                                                )                                                                                                  ⅆ                    t                                                                                                              ⅆ                      log                                        ⁢                                                                                  ⁢                                          I                      ⁡                                              (                                                  λ                          IR                                                )                                                                                                  ⅆ                    t                                                              ≅                            ⁢                                                                                          I                      ⁡                                              (                                                                              t                            2                                                    ,                                                      λ                            R                                                                          )                                                              -                                          I                      ⁡                                              (                                                                              t                            1                                                    ,                                                      λ                            R                                                                          )                                                                                                  I                    ⁡                                          (                                                                        t                          1                                                ,                                                  λ                          R                                                                    )                                                                                                                                  I                      ⁡                                              (                                                                              t                            2                                                    ,                                                      λ                            IR                                                                          )                                                              -                                          I                      ⁡                                              (                                                                              t                            1                                                    ,                                                      λ                            IR                                                                          )                                                                                                  I                    ⁡                                          (                                                                        t                          1                                                ,                                                  λ                          IR                                                                    )                                                                                                                                              =                            ⁢                                                                    [                                                                  I                        ⁡                                                  (                                                                                    t                              2                                                        ,                                                          λ                              R                                                                                )                                                                    -                                              I                        ⁡                                                  (                                                                                    t                              1                                                        ,                                                          λ                              R                                                                                )                                                                                      ]                                    ⁢                                      I                    ⁡                                          (                                                                        t                          1                                                ,                                                  λ                          IR                                                                    )                                                                                                            [                                                                  I                        ⁡                                                  (                                                                                    t                              2                                                        ,                                                          λ                              IR                                                                                )                                                                    -                                              I                        ⁡                                                  (                                                                                    t                              1                                                        ,                                                          λ                              IR                                                                                )                                                                                      ]                                    ⁢                                      I                    ⁡                                          (                                                                        t                          1                                                ,                                                  λ                          R                                                                    )                                                                                                                                              =                            ⁢              R                                                          (        7        )            Now defineThen describes a cluster of points whose slope of y versus x will give R.x(t)=[I(t2,λIR)−I(t1,λIR)]I(t1,λR)y(t)=[I(t2,λR)−I(t1,λR)]I(t1,λIR)   (8)y(t)=Rx(t)
The optical signal through the tissue can be degraded by both noise and motion artifact. One source of noise is ambient light which reaches the light detector. Another source of noise is electromagnetic coupling from other electronic instruments. Motion of the patient also introduces noise and affects the signal. For example, the contact between the detector and the skin, or the emitter and the skin, can be temporarily disrupted when motion causes either to move away from the skin. In addition, since blood is a fluid, it responds differently than the surrounding tissue to inertial effects, thus resulting in momentary changes in volume at the point to which the oximeter probe is attached.
Motion artifact can degrade a pulse oximetry signal relied upon by a physician, without the physician's awareness. This is especially true if the monitoring of the patient is remote, the motion is too small to be observed, or the doctor is watching the instrument or other parts of the patient, and not the sensor site.
In one oximeter system described in U.S. Pat. No. 5,025,791, an accelerometer is used to detect motion. When motion is detected, readings influenced by motion are either eliminated or indicated as being corrupted. In a typical oximeter, measurements taken at the peaks and valleys of the blood pulse signal are used to calculate the desired characteristic. Motion can cause a false peak, resulting in a measurement having an inaccurate value and one which is recorded at the wrong time. In U.S. Pat. No. 4,802,486, assigned to Nellcor, the assignee of the present invention, the entire disclosure of which is incorporated herein by reference, an EKG signal is monitored and correlated to the oximeter reading to provide synchronization to limit the effect of noise and motion artifact pulses on the oximeter readings. This reduces the chances of the oximeter locking onto a periodic motion signal. Still other systems, such as the one described in U.S. Pat. No. 5,078,136, assigned to Nellcor, the entire disclosure of which is incorporated herein by reference, use signal processing in an attempt to limit the effect of noise and motion artifact. The '136 patent, for instance, uses linear interpolation and rate of change techniques to analyze the oximeter signal.
Each of the above-described techniques for compensating for motion artifact has its own limitations and drawbacks. It is therefore desirable that a pulse oximetry system be designed which more effectively and accurately reports blood-oxygen levels during periods of motion.